List of top Mathematics Questions asked in MET

Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The number of persons in the room is

The area bounded by $y = 1 + \dfrac{8}{x^2}$ and the ordinates $x = 2$ and $x = 4$ is

If $f(x) = \begin{cases} x+1, & x \le 1 \\ 3 - ax^2, & x>1 \end{cases}$ is continuous at $x = 1$, then $a$ is

If $\sin(\pi \cos \theta) = \cos(\pi \sin \theta)$, then which of the following is correct?

If $3\sin^{-1}\!\left(\dfrac{2x}{1+x^{2}}\right) - 4\cos^{-1}\!\left(\dfrac{1-x^{2}}{1+x^{2}}\right) + 2\tan^{-1}\!\left(\dfrac{2x}{1-x^{2}}\right) = \dfrac{\pi}{3}$, then $x$ equals

The equation $(\cos p - 1)x^{2}+ (\cos p)\,x + \sin p = 0$ in the variable $x$ has real roots. Then $p$ can take values in the interval

By eliminating the arbitrary constants $A$ and $B$ from $y = Ax^{2} + Bx$, the differential equation obtained is

The least positive remainder when $123 \times 125 \times 127$ is divided by 124 is

If $f(x) = \dfrac{\log(1+ax) - \log(1-bx)}{x}$ for $x \neq 0$ and $f(0) = k$, and $f(x)$ is continuous at $x = 0$, then $k$ equals

Area of the triangle in the Argand diagram formed by the complex numbers $z$, $iz$, $z + iz$ where $z = x + iy$ is

$\displaystyle\int_{0}^{\pi/2} \dfrac{\sin^{n}\theta}{\sin^{n}\theta + \cos^{n}\theta}\,d\theta$ is equal to

The area in square units enclosed by the curve $x^{2}y = 36$, the $x$-axis and the lines $x = 6$ and $x = 9$ is

The general solution of $x\sqrt{1+y^{2}}\,dx + y\sqrt{1+x^{2}}\,dy = 0$ is

If $|f(x)|$ is continuous at $x = a$, then $f(x)$

The value of $a$ for which $f(x) = a\sin x + \dfrac{1}{3}\sin 3x$ has an extremum at $x = \dfrac{\pi}{3}$ is

The work done by the force $4\hat{i} - 3\hat{j} + 2\hat{k}$ in moving a particle along a straight line from the point $(3, 2, -1)$ to $(2, -1, 4)$ is

If $\mathbf{a}= -\hat{i} + 2\hat{j} - \hat{k}$, $\mathbf{b} = \hat{i} + \hat{j} - 3\hat{k}$ and $\mathbf{c} = -4\hat{i} - \hat{k}$, then $\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) + (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$ is

The product of the perpendiculars from $(-1, 2)$ to the pair of lines $2x^{2} - 5xy + 2y^{2} + 3x - 3y + 1 = 0$ is

If $(3 - x) \equiv (2x - 5) \pmod{4}$, then one of the values of $x$ is

Derivative of $x^{x}$ is

If $\left(\dfrac{1}{2},\,\dfrac{1}{3},\,n\right)$ are the direction cosines of a line, then the value of $n$ is

If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$, then $x + y + z$ is

The statement $P(n) = 9^{n} - 8^{n}$, when divided by 8, always leaves the remainder

In the group $G = \{0,1,2,3,4\}$ under $\times_5$, the inverse of $(2 \times_5 2^{-1})$ is}

The negation of the compound proposition $p \vee (\neg p \vee q)$ is